Factors temperature dependence of shift

In conclusion, the temperature dependence of shift factors for the networks studied here do not follow the WLF equation, but rather an Arrhenius-type relationship. The apparent activation energies are independent of stoichiometric variation [as they are when is varied by changing prepolymer molecular weight (13)]. ... 

One approach to find the parameters for equations 5 or 6 is by a b t fit of the DSC data. A more satisfying sq>proach may be to obtain the parameters from the temperature dependence of shift factors used to reduce isothermal data, where the shift factor is simply the difference between the In at the temperature of int est and the In at a... 

Figure 12.15 Stress relaxation master curve for PET/0.6PHB at the reference temperature 20 C (a) and temperature dependence of shift factor (b). The symbols in the master curve are the same as in Figure 12.14. (After [51].)...

TABLE 26.1. WLF parameters characterizing temperature dependencies of shift factors for relaxation and retardation times in various polymer systems. 

Fig. 128. Temperature dependence of shift factor (a,) obtained from the time-temperature shift for an amorphous LassAhjNijo alloy.

The viscosity of viscoelastic liquids at temperatures slightly above Tg can be determined by the procedures outUned above. Thus a step shear stress is imposed on the viscoelastic liquid at temperatures well above Tg, and once steady state is reached the sample is cooled to the temperature of interest then the straight line of J t) vs. t is recorded, and the viscosity is determined from the reciprocal of the slope of the straight line. By assuming that the elastic and viscous mechanisms have the same temperature dependence, the shift factor can be written in terms of the viscosity as (2,5)... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

Figure 4.10(b) shows the temperature dependence of the absorption spectrum expected for an indirect gap. It can be noted that the contribution due to becomes less important with decreasing temperature. This is due to the temperature dependence of the phonon density factor (see Equation (4.37)). Indeed, at 0 K there are no phonons to be absorbed and only one straight line, related to a phonon emission process, is observed. From Figure 4.10(b) we can also infer that cog shifts to higher values as the temperature decreases, which reflects the temperature dependence of the energy... 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

However, because measurements are kinetically determined, this is a less accurate form of the equation. Very often it is observed that the measured shift factors, defined for different properties, are independent of the measured property. In addition, if for every polymer system, a different reference temperature is chosen, and ap is expressed as a function of T — rj, then ap turns out to be nearly universal for all polymers. Williams, Landel and Ferry believed that the universality of the shift factor was due to a dependence of relaxation rates on free volume. Although the relationship has no free volume basis, the constants and may be given significance in terms of free volume theory (Ratner, 1987). Measurements of shift factors have been carried out on crosslinked polymer electrolyte networks by measuring mechanical loss tangents (Cheradame and Le Nest, 1987). Fig. 6.3 shows values of log ap for... 

Fig. 4.7 Temperature dependence of the mean relaxation time (r) divided by the rheological shift factor for the dielectric normal mode (plus) the dielectric segmental mode (cross) and NSE at Qinax=l-44 A (empty circle) and Q=1.92 A (empty square) [7] (Reprinted with permission from [8]. Copyright 1992 Elsevier)...

Fig. 4.9 Temperature dependence of the characteristic time of the a-relaxation in PIB as measured by dielectric spectroscopy (defined as (2nf ) ) (empty diamond) and of the shift factor obtained from the NSE spectra at Qmax=l-0 (filled square). The different lines show the temperature laws proposed by Tormala [135] from spectroscopic data (dashed-dotted), by Ferry [34] from compliance data (solid) and by Dejean de la Batie et al. from NMR data (dotted) [136]. (Reprinted with permission from [125]. Copyright 1998 American Chemical Society)...

Fig. 4.11 Temperature dependence of the shift factors as reported in the literature for atactic polypropylene 1 dynamic mechanical measurements [140], 2 NMR data of Pschorn et al. [141], 3 photon correlation spectroscopy [142], 4 from NMR measurements of Moe...

In summary, the temperature dependence of the proton nmr spectra does not provide a sufficient basis to decide upon the norbornyl cation structure. The slow 3,2-hydride shift might be rationalized by either a non-classical or classical interpretation, but both the activation energies and the pre-exponential factors might be influenced by solvation. If this is the case the arguments based on the pmr observations become still less persuasive. 

The Arrhenius-like temperature dependence obtained, which however gives rise to unreasonable Irequency factors, can then be rationalized on the basis of the temperature dependence of the blackbody radiation. At higher temperatures, the energy density per unit wavelength of the blackbody radiation increases with the maximum in the distribution shifted to higher frequency. Also, at a given frequency the intensity of radiation emitted varies approximately as In / oc -T" Therefore, as the temperature increases, so too does the intensity of the radiation and with it the rate of energization of the cluster ion and, consequently, the rate of unimolecular dissociation. Thus the temperature dependence is entirely consistent with a radiative mechanism for dissociation. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

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